SOLUTION: Please help me solve this problem: The sum of the reciprocals of two numbers is 7 and the difference of their reciprocals is 3. What are the number? Thanks..

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Question 585595: Please help me solve this problem:
The sum of the reciprocals of two numbers is 7 and the difference of their reciprocals is 3. What are the number?
Thanks..
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be a and b
given:
(1) +1%2Fa+%2B+1%2Fb+=+7+
(2) +1%2Fa+-+1%2Fb+=+3+
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Just add the equations
+2%2A%28+1%2Fa+%29+=+10+
+2+=+10a+
+a+=+1%2F5+
and
(1) +1%2Fa+%2B+1%2Fb+=+7+
(1) +5+%2B+1%2Fb+=+7+
(1) +1%2Fb+=+2+
(1) +b+=+1%2F2+
The numbers are 1/5 and 1/2